The Rare Disease Test
A disease affects 1% of a population. A test is 99% sensitive (it detects the disease when present) and 99% specific (it is negative when the disease is absent). You test positive. What is the probability you actually have the disease?
Related problems
Source: Base-rate neglect in medical testing; the canonical framing follows Casscells, Schoenberger and Grayboys (1978). Statement written for AxiomIQ.